Linear Systems: Non-Fragile Control and Filtering presents the latest research results and a systematic approach to designing non-fragile controllers and filters for linear systems. The authors combine the algebraic Riccati technique, the linear matrix inequality (LMI) technique, and the sensitivity analysis method to establish a set of new non-fragile (insensitive) control methods. This proposed method can optimize the closed-loop system performance and make the designed controllers or filters tolerant of coefficient variations in controller or filter gain matrices.
A Systematic Approach to Designing Non-Fragile Controllers and Filters for Linear Systems: The text begins with developments and main research methods in non-fragile control. It then systematically presents novel methods for non-fragile control and filtering of linear systems with respect to additive/multiplicative controller/filter gain uncertainties. The book introduces the algebraic Riccati equation technique to solve additive/multiplicative norm-bounded controller/filter gain uncertainty, and proposes a structured vertex separator to deal with the numerical problem resulting from interval-bounded coefficient variations. It also explains how to design insensitive controllers and filters in the framework of coefficient sensitivity theory. Throughout, the book includes numerical examples to demonstrate the effectiveness of the proposed design methods.
More Effective Design Methods for Non-Fragile Controllers and Filters: The design and analysis tools described will help readers to better understand and analyze parameter uncertainties and to design more effective non-fragile controllers and filters. Providing a coherent approach, this book is a valuable reference for researchers, graduate students, and anyone who wants to explore the area of non-fragile control and filtering.
Author(s): Guang-Hong Yang, Xiang-Gui Guo, Wei-Wei Che, Wei Guan
Publisher: CRC Press
Year: 2013
Language: English
Pages: xiv+278
Tags: Приборостроение;Обработка сигналов;
Linear Systems: Non-Fragile Control and Filtering......Page 4
Contents......Page 6
Preface......Page 10
Symbol Description......Page 14
1 Introduction......Page 16
2.1 Delta Operator Definition......Page 22
2.2 H∞ Performance Index......Page 23
2.3 Operations on Systems......Page 24
2.4 Some Other Definitions and Lemmas......Page 26
3.2 Problem Statement......Page 34
3.3.1 Additive Controller Gain Uncertainty Case......Page 37
3.3.2 Multiplicative Controller Gain Uncertainty Case......Page 41
3.4 Example......Page 49
3.5 Conclusion......Page 50
4.1 Introduction......Page 52
4.2 Problem Statement......Page 53
4.3.1 Additive Controller Gain Uncertainty Case......Page 56
4.3.2 Multiplicative Controller Gain Uncertainty Case......Page 63
4.4 Example......Page 72
4.5 Conclusion......Page 75
5.1 Introduction......Page 76
5.2 Problem Statement......Page 77
5.3.1 Additive Gain Uncertainty Case......Page 79
5.3.2 Multiplicative Gain Uncertainty Case......Page 88
5.4 Example......Page 97
5.5 Conclusion......Page 98
6.1 Introduction......Page 100
6.2.1 Problem Statement......Page 101
6.2.2 Non-Fragile H∞ Controller Design Methods......Page 102
6.2.3 Example......Page 114
6.3 Non-Fragile H∞ Controller Design for Continuous-Time Systems......Page 118
6.3.2 Non-Fragile H∞ Controller Design Methods......Page 119
6.3.3 Example......Page 125
6.4.1 Problem Statement......Page 129
6.4.2 Sparse Structured Controller Design......Page 134
6.4.3 Example......Page 139
6.5 Conclusion......Page 143
7.1 Introduction......Page 146
7.2.1 Problem Statement......Page 147
7.2.2 Non-Fragile H∞ Filter Design Methods......Page 148
7.2.3 Example......Page 157
7.3.1 Problem Statement......Page 160
7.3.2 Non-Fragile H∞ Filter Design Methods......Page 161
7.3.3 Example......Page 166
7.4.1 Problem Statement......Page 170
7.4.2 Non-Fragile H∞ Filter Design with Sparse Structures......Page 175
7.4.3 Example......Page 179
7.5 Conclusion......Page 181
8.1 Introduction......Page 182
8.2 Problem Statement......Page 183
8.3 Insensitive H∞ Filter Design......Page 187
8.3.1 Additive Filter Coefficient Variation Case......Page 188
8.3.2 Multiplicative Filter Coefficient Variation Case......Page 192
8.4 Computation of Robust H∞ Performance Index......Page 195
8.5 Comparison with the Existing Design Method......Page 197
Additive Coefficient Variations Case......Page 198
Multiplicative Coefficient Variations Case......Page 200
8.7 Conclusion......Page 204
9.1 Introduction......Page 206
9.2 Problem Statement......Page 207
9.3.1 Additive Coefficient Variation Case......Page 213
9.3.2 Multiplicative Filter Coefficient Variation Case......Page 217
Additive Coefficient Variation Case......Page 221
Multiplicative Coefficient Variation Case......Page 222
9.5 Conclusion......Page 225
10.1 Introduction......Page 226
10.2 Problem Statement......Page 227
10.3 Insensitive H∞ Tracking Control Design......Page 233
10.4 Example......Page 235
10.5 Conclusion......Page 240
11.1 Introduction......Page 242
11.2.1 Sensitivity Function......Page 243
11.3.1 Step 1: General Conditions for the Existence of Insensitive H∞ Controllers......Page 246
11.3.2 Step 2: Non-Fragile H∞ Controller Design with Interval-Bounded Controller Coefficient Variations......Page 251
11.3.3 Summary of the Approach......Page 258
11.3.4 Insensitive H∞ Control with Multiplicative Controller Coefficient Variations......Page 259
11.4 Example......Page 267
Multiplicative Coefficient Variation Case......Page 268
Additive Coefficient Variation Case......Page 270
11.5 Conclusion......Page 273
Bibliography......Page 278
Index......Page 292
